A micelle model for the sedimentation behavior of bovine beta-casein

The monomer-single polymer model of G.A. Gilbert (Disc. Faraday Soc. 20 (1955) 68) for moving boundary sedimentation has been used by Payens and colleagues to explain the observed results for bovine caseins, and by Harrington and colleagues to explain the observed results for myosin fibrils. Electron microscope pictures of Buchheim and Schmidt have subsequently revealed micellar beta-casein in the form of slightly elongated or spherical particles having a bimodal size distribution, but with a broad range of particle sizes, at concentrations not too far above the critical micelle concentration. The equilibrium properties of a broadly distributed micellar system can be fitted by the shell model developed by one of us, and in the present article, the shell model is extended to predict the moving boundary sedimentation behavior of such a system. The observed sedimentation patterns, as well as the critical concentration predictions of the monomer-single polymer Gilbert sedimentation model, are satisfactorily described with the present model, based on a continuous distribution of intermediates between monomers and the largest possible spherical micelles. For one example considered, the predicted frequency distribution of molecular weight is in qualitative agreement with the frequency distribution of particle volume found by Buchheim and Schmidt.     

Molecular Dynamics Simulation of a Micellar System

We present the results of an atomistic molecular dynamics simulation based on the AMBER/OPLS force field applied to segments of isolated one-dimensional micelles, 2,3,6,7,10,11-Hexa-(1,4,7-Trioxaoctyl)-Triphenylene, in aqueous solution using the SPC/E water model. The quantities which we study include the intra-micellar monomer structure, e.g., the equilibrium monomer-monomer separation along the micelle, the micelle-water interface, which yields the effective micellar diameter, and the flexibility of the micelle in terms of its persistence length as a function of temperature. In addition, we determine the micelle size distribution at low concentration via the free enthalpy gain per monomer-monomer contact using a hydration shell model in combination with thermodynamic integration. Finally, we locate the isotropic-to-nematic transition by using our results as input for an analytical model.     

The effect of the propagation coefficient on size distribution in micellar systems

In this study the effect of the propagation coefficient on the molar distribution function in a modified shell model for micellar systems was examined. The sharpness of the micelle size distribution boundary was found to depend less on the degree of polymerization, n, than on the propagation coefficient, P. Although Kegeles (J. Phys. Chem. 83 (1979) 1728) has reported a marked sharpening of the distribution boundary when P = 2.0. we found the boundary to be fairly broad at this point. However, as values of the propagation coefficient were increased from 3 to 10, the micelle distribution boundary became increasingly sharp. The possibility of such a change in the reaction boundary arising from a structural transition, accompanied by a change in the rate of dissociation of monomer from the shell, is also discussed.     

Effect of calcium on kinetic and structural aspects of dilution-induced micellar to lamellar phase transformation in phosphatidylcholine-cholate mixtures

Previously, we have shown [Almog, S., Kushnir, T., Nir, S., & Lichtenberg, D. (1986) Biochemistry 25, 2597-2605] that the distribution of cholate between phosphatidylcholine (PC) vesicles and aqueous media apparently obeys a single distribution coefficient, K. In PC-cholate mixed micellar systems, the monomer concentration does not rise much above the cholate's critical micelle concentration (cmc). Consequently, for vesicular systems, the cholate:PC molar ratio in the mixed aggregates (Re) is given by Re = [cholate]/([PC] + 1/K) whereas for mixed micellar systems Re = ([cholate] - cmc)/[PC]. Dilution of mixed micellar systems results in a decrease of Re, due to an increase in the fraction of monomeric PC. If the decrease in Re is to values lower than 0.3, micellar to lamellar transformation occurs. This process involves a sequence of three steps, namely, micellar equilibration followed by vesiculation and subsequent vesicle size growth via a lipid transfer mechanism. The ultimate size of the resultant vesicles is an increasing function of Re. This work is devoted to the effect of calcium on the dilution-induced vesicle formation. Its major findings and conclusions are as follows: (i) Calcium reduces the cmc of the detergent and raises its distribution coefficient between PC vesicles and the aqueous medium. Thus, for any given cholate and PC concentrations, calcium causes an increase of Re. (ii) The rate of all the steps which ultimately lead to an apparent equilibrium vesicle size distribution increases dramatically with increasing calcium concentration. Thus, equilibration is attained in seconds to minutes rather than many hours required in the absence of calcium.(ABSTRACT TRUNCATED AT 250 WORDS)     

Complexities of Particulate Matter Measurement in Parenteral Formulations of Small-Molecule Amphiphilic Drugs

Reconstituted parenteral solutions of three surface-active anti-infective small-molecule drugs and solutions of sodium dodecyl sulfate (SDS, a model surfactant) were studied to quantify the impact of sample preparation and handling on particle counts. Turbidimetry and light obscuration profiles were recorded as a function of agitation and shearing with and without the introduction of foam into the solutions. SDS solutions at concentrations above the critical micelle concentration (CMC) show significantly greater sensitivity to shear and foam presence than SDS solution below the CMC: Values of >10 μm particles increased 8 fold over control (an unsheared sample) in the micellar solution vs. 4 fold particle count increase over control at a sub-micellar concentration. An even more significant increase in the ratio of particle count in sheared/unsheared solution is seen for >25 μm unit counts, due to the increased interference of foam with the measurement. Two commercial products, injection formulations of teicoplanin and cefotaxime sodium, as well as an investigational compound 1, showed an increase in scattering as a function of foam production. The impact of foaming was significant, resulting in an increase of turbidity and light obscuration measurements in all solutions. The results illustrate some of the challenges that are inherent to optically clear, homogeneous pharmaceutical injections containing compounds which have a tendency toward self-association and surfactant-like behavior.     

Characterization of the solubilization of lipid bilayers by surfactants

This communication addresses the state of aggregation of lipid-detergent mixed dispersions. Analysis of recently published data suggest that for any given detergent-lipid mixture the most important factor in determining the type of aggregates (mixed vesicles or mixed micelles) and the size of the aggregate is the detergent to lipid molar ratio in these aggregates, herein denoted the effective ratio, Re. For mixed bilayers this effective ratio has been previously shown to be a function of the lipid and detergent concentrations and of an equilibrium partition coefficient, K, which describes the distribution of the detergent between the bilayers and the aqueous phase. We show that, similar to mixed bilayers, the size of mixed micelles is also a function of the effective ratio, but for these dispersions the distribution of detergent between the mixed micelles and the aqueous medium obeys a much higher partition coefficient. In practical terms, the detergent concentration in the mixed micelles is equal to the difference between the total detergent concentration and the critical micelle concentration (cmc). Thus, the effective ratio is equal to this difference divided by the lipid concentration. Transformation of mixed bilayers to mixed micelles, commonly denoted solubilization, occurs when the surfactant to lipid effective ratio reaches a critical value. Experimental evaluation of this critical ratio can be based on the linear dependence of detergent concentration, required for solubilization, on the lipid concentration. According to the 'equilibrium partition model', the dependence of the 'solubilizing detergent concentration' on the lipid concentration intersects with the lipid axis at -1/K, while the slope of this dependence is the critical effective ratio. On the other hand, assuming that when solubilization occurs the detergent concentration in the aqueous phase is approximately equal to the critical micelle concentration, implies that the above dependence intersects with the detergent axis at the critical micelle concentration, while its slope, again, is equal to the critical effective ratio. Analysis of existing data suggests that within experimental error both these distinctively different approaches are valid, indicating that the critical effective ratio at which solubilization occurs is approximately equal to the product of the critical micelle concentration and the distribution coefficient K. Since the nature of detergent affects K and the critical micelle concentration in opposite directions, the critical ('solubilizing') effective ratio depends upon the nature of detergent less than any of these two factors.     

Micelle formation of bile salts and zwitterionic derivative as studied by two-dimensional NMR spectroscopy

The self-association of sodium taurodeoxycholate (NaTDC) and a zwitterionic derivative of cholic acid (CHAPS) in deuterium oxide was investigated by one- and two-dimensional nuclear magnetic resonance spectroscopy (NMR) spectroscopy. Analysis of the concentration dependence of the chemical shifts of several protons suggested that NaTDC and CHAPS form nonamers and heptamers, respectively, as well as dimer. The equilibrium constants of dimerization and the micellar aggregation numbers are close to the literature values. From the intensities of intermolecular cross-peaks in the nuclear Overhauser effect spectroscopy (NOESY) and rotating frame nuclear Overhauser effect spectroscopy (ROESY) spectra of NaTDC and CHAPS micellar solutions, partial structures of their micelles were estimated. The CHAPS micelle consists mainly of the back-to-back association, similarly to taurocholate (NaTC). However, the NaTDC micelle consists of the back-to-face association, because the face of NaTDC is rather hydrophobic. Furthermore, the back of bile molecules forms a convex plane and the face forms a concave plane. The back-to-face structure of NaTDC will be stabilized by a close contact between these planes. The chemical shift changes of several protons of CHAPS and NaTC in the micellar state are close to each other, but are different from those of NaTDC. This finding is consistent with the difference in their micellar structures.     

Characterization of the solubilization of lipid bilayers by surfactants

This communication addresses the state of aggregation of lipid-detergent mixed dispersions. Analysis of recently published data suggest that for any given detergent-lipid mixture the most important factor in determining the type of aggregates (mixed vesicles or mixed micelles) and the size of the aggregate is the detergent to lipid molar ratio in these aggregates, herein denoted the effective ratio, R_e. For mixed bilayers this effective ratio has been previously shown to be a function of the lipid and detergent concentrations and of an equilibrium partition coefficient, K, which describes the distribution of the detergent between the bilayers and the aqueous phase. We show that, similar to mixed bilayers, the size of mixed micelles is also a function of the effective ratio, but for these dispersions the distribution of detergent between the mixed micelles and the aqueous medium obeys a much higher partition coefficient. In practical terms, the detergent concentration in the mixed micelles is equal to the difference between the total detergent concentration and the critical micelle concentration (cmc). Thus, the effective ratio is equal to this difference divided by the lipid concentration. Transformation of mixed bilayers to mixed micelles, commonly denoted solubilization, occurs when the surfactant to lipid effective ratio reaches a critical value. Experimental evaluation of this critical ratio can be based on the linear dependence of detergent concentration, required for solubilization, on the lipid concentration. According to the ‘equilibrium partition model’, the dependence of the ‘solubilizing detergent concentration’ on the lipid concentration intersects with the lipid axis at −1/K, while the slope of this dependence is the critical effective ratio. On the other hand, assuming that when solubilization occurs the detergent concentration in the aqueous phase is approximately equal to the critical micelle concentration, implies that the above dependence intersects with the detergent axis at the critical micelle concentration, while its slope, again, is equal to the critical effective ratio. Analysis of existing data suggests that within experimental error both these distinctively different approaches are valid, indicating that the critical effective ratio at which solubilization occurs is approximately equal to the product of the critical micelle concentration and the distribution coefficient K. Since the nature of detergent affects K and the critical micelle concentration in opposite directions, the critical (‘solubilizing’) effective ratio depends upon the nature of detergent less than any of these two factors.     

Monomer-micelle transition of the ganglioside GM1 and the hydrolysis by Clostridium perfringens neuraminidase.

The action of Clostridium perfringens neuraminidase on the ganglioside Gm1 tritiated in the ceramide moiety was studied. The rates of hydrolysis of the Gm1 ganglioside were determined from radioactivity in the neutral glycolipid product, which was separated from the substrate on DEAE-Sephadex columns. In order to study the physical state of the substrate in the conditions used in the neuraminidase treatment, the critical micelle concentrations of the Gm1 ganglioside were determined using formation of the triiodide anion in aqueous iodine solution as an indicator. The critical micelle concentrations were also obtained by determining the non-sedimenting radioactivity at different concentrations of the labeled ganglioside per total volume used in ultracentrifugation experiments. In addition, the concentrations of the monomeric ganglioside were concluded from the results of the ultra-centrifugation studies. The increase in the reaction rate of the Gm1 hydrolysis as the function of the substrate concentration was leveled off at 25-28 microM ganglioside. The abrupt change at this concentration is interpreted as reflecting the monomer-micelle transition of the ganglioside in the conditions used (50mM sodium acetate buffer, pH 4.6). The critical micelle concentration was 29 microM on the basis of the triiodide test, and ultracentrifugation revealed the critical micelle concentration 28 microM. The reaction velocity of the hydrolysis was decreased immediately above the critical micelle concentration, and became constant at higher concentrations of the ganglioside. A close correlation to these changes in the reaction rate is suggested to exist in the concentrations of the monomeric Gm1 ganglioside. Saturation of the buffer used in the neuraminidase assays with butanol effected a striking change in the plot of reaction rate versus ganglioside concentration. The reaction rate increased up to 100-110 microM Gm1 ganglioside. The shift of the inflexion point in the rate plot from 25-28 microM to 100-110 microM ganglioside concentration is suggested to be due to a respective change in the critical micelle concentration effected by butanol. N-Acetylneuraminyllactosyl ceramide, lactosyl ceramide and asialo-Gm1 ganglioside had an inhibitory effect on the reaction. In contrast, N-acetylneuraminyllactose, lactose and some other free saccharides were not inhibitory. The results demonstrate that factors other than the saccharide structure must be taken into account when substrate specificity of a glycosidase is studied using competition experiments. It is suggested that the inhibition effected by the glycolipids is due to an increase in the micellar state of the Gm1 ganglioside.     

Preferential ligand binding to multi-state acceptor systems: the unexplored paradox of acceptor self-association that is ligand-mediated but detrimental to ligand binding

Consideration is given to the interactions of ligand with self-associating acceptor systems for which preferential ligand binding is an ambiguous term, in that the acceptor species with greater affinity for ligand possesses relatively fewer binding sites. A paradoxical situation wherein ligand-mediated self-association is seemingly detrimental to ligand binding is shown to be the predicted outcome for a transient range of ligand concentrations. This outcome reflects the existence of a critical point in the dependence of the extent of acceptor self-association upon ligand concentration that coincides with a cross-over point of ligand-binding curves for different, fixed total concentrations of acceptor. By classical differentiation methods the conditions for the existence of these critical points are established not only for two-state acceptor systems but also for three-state acceptor systems in which the ligand-binding form of monomer also undergoes reversible isomerization to an inactive state. Similar procedures are used to comment upon the forms of binding curves for the three-state acceptor systems, the Scatchard representations of which may exhibit as many as three critical points (two maxima and a minimum). This delineation of quantitative expressions for critical points and other distinctive features associated with the conflicting interplay of ligand-binding and self-association behaviour should provide a more definitive means of characterizing systems with one acceptor state the preferred binding form on affinity grounds but with the other the preferred state from the viewpoint of binding-site numbers.     

Synthesis and physical characterization of poly(ethylene glycol)-gelatin conjugates

Poly(ethylene glycol) (PEG) with the terminal group of active ester was coupled to the amino group of gelatin to prepare PEG-grafted gelatin (PEG-gelatin). The affinity chromatographic study revealed that the PEG-gelatin with high degrees of PEGylation did not adsorb onto the gelatin affinity column, in remarked contrast to gelatin alone and the PEG-gelatin with low PEGylation degrees. The former PEG-gelatin showed a critical micelle concentration while it had the apparent molecular size of about 100 nm and a surface charge of almost zero. These findings indicate that the PEG-gelatin formed a micelle structure of which the surface is covered with PEG molecules grafted. When the body distribution of 125I-labeled gelatin and PEG-gelatin after intravenous injection was evaluated, the radioactivity of micellar PEG-gelatin was retained in the blood circulation compared with that of gelatin and the PEG-gelatin of no micelle formation. At the same PEGylation degree, the blood concentration was significantly higher for the PEG-gelatin prepared from PEG with a molecular weight of 12 000 than that of molecular weights of 2000 and 5000. It is concluded that the PEG-gelatin is a drug carrier with a micelle structure which retains in the blood circulation.     

Critical micelle concentrations of gangliosides

The micellar properties of mixed, bovine gangliosides and purified galactosyl-N-acetylacetylgalactosaminyl (N-acetylneuraminyl) galactosylglucosylceramide were studied by gel filtration, equilibrium dialysis, and band and boundary centrifugation in sucrose gradients. The dissociation of micelles is very slow (days) in water and required us to approach equilibrium by association of monomers rather than by the dissociation of micelles. The gangliosides were therefore first converted into very low molecular weight aggregates (1-3 molecules) by dissolving them in Me2SO. Galactosyl-N-acetylgalactosaminyl(N-acetylneuraminyl)galactosylglucosylceramide was then diluted into aqueous sucrose gradients and sedimented by the boundary centrifugation technique. This gave a sedimenting micelle and a nonsedimenting monomer concentration of (1-2) x 10-10 M (or less) which corresponds to the critical micelle concentration value. The mixed gangliosides revealed two micellar sizes (i.e., 10 and 4.5 S), the slower sedimenting species being formed from the larger one with time (days). The critical micelle concentration of the mixed gangliosides was found to be approximately 10-8 M by a gel filtration, equilibrium dialysis, and band centrifugation.     

Determination of the aggregation number of detergent micelles using steady-state fluorescence quenching.

The development of a simple, reliable method for determination of detergent micelle aggregation number that relies solely on measurement of steady-state fluorescence quenching is presented. The degree of steady-state fluorescence quenching of a micelle-solubilized fluorophore (pyrene) by a quencher that partitions greatly into the micelles (coumarin 153) is dependent on the micelle concentration, which can therefore be determined. The aggregation number is calculated as the micelle concentration/detergent monomer concentration (the total detergent concentration above the critical micelle concentration). For the determination to be accurate, the partition coefficient of the quencher into the micelle phase is determined and used to calculate the micellar concentration of quencher. Also, the quenching of pyrene by a coumarin 153 molecule within the same micelle must be complete, and this was confirmed by time-resolved fluorescence measurements. Aggregation numbers were determined for one cationic and several nonionic detergents and were found to be consistent with literature values. The approach presented is an improvement on a previous luminescence quenching technique (Turro, N.J., and A. Yekta. 1978. J. Am. Chem. Soc. 100:5951-5952) and can be used on cationic, anionic, and nonionic detergents with micelles ranging greatly in size and under varying conditions, such as detergent concentration, ionic strength, or temperature.     

Interaction of indole and tryptophan derivatives with sodium dodecyl sulfate micelles measured with ultraviolet absorption and fluorescence quenching

The distribution of indole and tryptophan derivatives between sodium dodecyl sulfate (SDS) micellar and aqueous phases was analyzed using conventional methods of ultraviolet (UV) absorption spectroscopy and measurement of fluorescence quenching by succinimide. On the assumption of a simple pseudo-phase equilibrium between both phases the distribution coefficient was easily obtained by the measurement of the ratioR _pv of the absorbance intensity in the peak to that in the valley of the UV spectra or the fluorescence quenching constant K_sv. The possibilities and limitations of utilizing the ratio of the collisional quenching constant estimating from theK _sv value in the micellar phase to that in the aqueous phase for a measure of the polarity of the microenvironment around the tryptophan derivatives in the SDS micelle is discussed in comparison with theR _pv values for the UV spectra. The indole ring in the derivatives in the SDS micelle is localized near or on the micelle-water interface with its imino group directed toward the aqueous phase. Thus it can serve as a feasible model for interpreting the distribution coefficients andR _pv values obtained for the various indole and tryptophan derivatives.Abbreviations UV ultraviolet - SDS sodium dodecyl sulfate - ATEE N-acetyl-l-tryptophan ethyl ester - ATA N-acetyl-l-tryptophan-amide - CMC critical micelle concentration     

Shell-cross-linked micelles containing cationic polymers synthesized via the RAFT process: toward a more biocompatible gene delivery system

Block copolymers poly(2-(dimethylamino) ethyl methacrylate)-b-poly(polyethylene glycol methacrylate) (PDMAEMA-b-P(PEGMA)) were prepared via reversible addition fragmentation chain transfer polymerization (RAFT). The polymerization was found to proceed with the expected living behavior resulting in block copolymers with varying block sizes of low polydispersity (PDI <1.3). The resulting block copolymer was self-assembled in an aqueous environment, leading to the formation of pH-responsive micelles. Further stabilization of the micellar system was performed in water using ethylene glycol dimethacrylate and the RAFT process to cross-link the shell. The cross-linked micelle was found to have properties significantly different from those of the uncross-linked block copolymer micelle. While a distinct critical micelle concentration (CMC) was observed using block copolymers, the CMC was absent in the cross-linked system. In addition, a better stability against disintegration was observed when altering the ionic strength such as the absence of changes of the hydrodynamic diameter with increasing NaCl concentration. Both cross-linked and uncross-linked micelles displayed good binding ability for genes. However, the cross-linked system exhibited a slightly superior tendency to bind oligonucleotides. Cytotoxicity tests confirmed a significant improvement of the biocompatibility of the synthesized cross-linked micelle compared to that of the highly toxic PDMAEMA. The cross-linked micelles were taken up by cells without causing any signs of cell damage, while the PDMAEMA homopolymer clearly led to cell death.     

Interactions of colipase with bile salt micelles. 2. Study by dialysis and spectrophotometry.

The finding reported in the preceding paper that colipase is able to bind one sodium taurodeoxycholate micelle per molecule was confirmed by dialysis and spectrophotometry. Dialysis in the presence of labelled sodium taurodeoxycholate provided a direct qualitative proof of taurodeoxycholate binding to colipase. This binding was found to occur only above the critical micelle concentration. But, dialysis did not give any information about the composition of the associations, because equilibrium was not attained at the end of the assays. Addition of sodium taurodeoxycholate above the critical micelle concentration was also observed to induce a strong perturbation of the ultraviolet spectrum of one or several of the three tyrosines of colipase. The variation of the perturbation as a function of sodium taurodeoxycholate concentration was consistent with the binding of a single micelle to colipase. The dissociation constant calculated in "micelle molarity" was approximately 1 X 10(-4) M. The colipase-bile salt micelle association can fix one molecule of lipase to form a ternary complex which represents an interesting model of a protein-protein interaction mediated by an organized lipid structure. The ternary complex is probably also a model for lipase-substrate interactions in the presence of an amphipath.     

Pressure-jump kinetics of bovine beta-casein micellization

Two samples of highly purified bovine beta-casein supplied to us by Dr. T.A.J. Payens of the National Institute for Dairy Research, Ede, The Netherlands, were studied over a range of concentration from just below the critical micelle concentration (CMC) to 0.46%, in 0.2 ionic strength phosphate buffer (pH 7.0), at 20 and 25 degrees C. The relaxation process studied by pressure jump using a 90 degree scattered light detector was also confirmed by the temperature-jump method. In the pressure-jump experiments, the process could be separated into two general time domains, with an approximate ratio of 10-25:1, a behavior reminiscent of that found for synthetic micellar systems. The faster relaxation process was still exhibited below the CMC, however. The concentration dependence of the faster relaxation time agreed very satisfactorily with predictions from the micelle model described in the companion paper.     

Growth of linear charged micelles

The electrostatics of micellar growth is reviewed and extended for solutions containing excess salt. In dilute solution the expansion of a linear micelle with increasing salt concentration is explained for a wide range of ionic strength. When the micellar charge density is very high, counterions condense nonuniformly onto the micellar rod. In that case the micelle may contract upon the addition of salt. In semidilute solutions the excluded-volume effect is an additional factor complicating the ionic strength dependence of micellar growth.     

Gelatin-alpha olefin sulfonate interactions studied by dynamic light scattering

Dynamic light scattering (DLS) measurements were performed to study the binding of anionic surfactant alpha olefin sulfonate (AOS) to gelatin chains at various NaCl concentrations at 30 degrees C in aqueous sodium phosphate buffer (pH = 6.8) solutions. The surfactant concentration was varied from 0 to 80 mM and the NaCl concentrations chosen were 0.025, 0.05, and 0.1 M. AOS exhibited electrostatic binding to the positively charged sites of the polypeptide chain resulting in considerable reduction in its hydrodynamic radius up to critical micellar concentration (cmc = 8 mM for no salt, 0.01 and 0.025 M, and 5 mM for 0.05 M and 2 mM for 0.1 M solutions). The correlation function revealed the presence of two types of structures above cmc; namely the micelles of AOS and gelatin-AOS micelle complexes. The micellar radii (Rm), the effective gelatin-surfactant complex radii (Rc), have been determined as a function of salt concentration. No critical aggregation concentration (cac) was observed. The inter-gelatin-surfactant complex (kD1) and inter-micellar interactions (kD2), were determined by fitting the concentration dependence of Rm and Rc to a virial expansion in reduced concentration (c - cmc), which are compared. While kD1 showed strong ionic strength dependence, kD2 remained invariant of the same. The protein to surfactant binding ratio was found to be smaller than normal. Results have been discussed within the framework of the necklace-bead model of polymer-surfactant interactions.